THE ANALYSIS

ENGINEERING STRUCTURES

BY

A. J. S. PIPPARD, M.B.E., D.Sc. MEMBEE OP 1'HE ~ 9 ~ ~ 1 0 N OF CIVIL ENGINEERS : MEMBER OF THE

AMF,EICAN SOCIETY OP OLVlL ENGINEERS ; PELLOW OF THE ROYAL AERONAUTICAL SOCIETY.

PROFESWR OF CIVIL ENOINzERlNO IN W E UNNUISlTY OP LONDON AT N P E R U L COLLEGE

nnd

J. F. BAKER, O.B.E., M.A., Sc.D. (Cantah.), D.Sc. (Wales).

ASSOCIATE MEMBER 08 TXB INSTITUTlDN OS clvn wamssas; ASSOCIATE M8MBgs. OP THE AMERICAN SDElaPY On ClYlL BNCMPBIB;

WBMBBR OF THE MSTllUTlON OP -UCNlUL mCMBxm. PROBEWR OP MECHANICAL SCIENCES IN THF UNlvERSL7Y On OAMBRmOE

POaMBRLY TPW(NIC*L PIRCBR TO TBS m SIRUCTURlg

-CH COMMrTl'BE.

LONDON

EDWARD ARNOLD & CO.

CONTENTS

CHAPTER 1

DEFINITIONS AND GENERAL PRINCIPLES PAGE

1.1. 1ntroduotion.-1.2. Claseification of etrudures.-1.3. Factor of safety and load factor.-1.4. Frameworks.-1.5. Criterion for frnmeworks.- 1.6. Resct~ve f0oroea.-1.7. Primary and secondnry stresses.-1.8. SelfSelf straining . 1

CHAPTER 2

1 PRIMARY STRESS ANALYSIS OF STATICALLY DETERbfINATE FRAMES

! 2.1. The general problem.-2.2. The atross diagram.-2.3. Ritter's method l of sections.-2.4. Method of resolution et joints.-2.5. Method of I tension caeffioienta . . . 7

i CHAPTER 3

THE STRESES IN STRAIGHT AND CURVED BEAMS

3.1: Shearing force and bending moment.-3.2. Relationship between loading, ahearing force snd bending moment.-3.3. Thwry of aimple bending.-3.4. Moment of resiatance.3.5. S t rww when loada sre not normal to the beam.3.0. Unnymmetricsl bending.3.7. Diatribu- tion of shear streas.3.8. Deflection of beams.3.9. Uniformly loaded cantilsver.4.10. Simply supported beam carrying a concentrated load. 3 . 1 1 . Simply supported beam oarrying a distributed 14.-3.12. Sim- ply supported beam subjected to a oouple applied st a point.3.13. Simply supported heam subjeotad to tramverse loads and end couples. -3.14. Enoastd beam.3.16. Beams of verying section subjected to any load system.-3.16. Moment area and shear a m methods-3.17. Bending stresses in ourved beema . . . 21

CHAPTER 4 THEOREMS RELATING TO ELASTIC BODIES

4.1. Elastic hehnvionr.4.2. Principle of anperpAsitian.4.3. Strain energy. 4 . 4 . Force in a bar in teFma of end diaphmenta.4.5. Strain energy aa s function of external loada4.0. Strsin energy due to bending.4.7. Strain energy due to shearing foroe.4.8. Strain energy due,to tomion.4.9. The strain energy of curved beama.4.10. Clerk Maxwell's reciprocal theorem.4.11. The first theorem of C&i&uo.4.12. The second theorem of C&iglinno.4.I3. Differential weffioienta of strain energy with reapeet to a moment.- 4.14. Principle of Saint Venant.4.15. Strain energy equations in terms of tension ooefficients , . . . . . 48

CONTENTS

CHAPTER 5

DISPLACEMENTS OF ELASTIC BODIES PAGE

6.1. Diaplsoement of the point of application of a single load.4.2. Din- placements by the firat theorem of Castiilinno.-5.3. Displacement of an unloeded ooint.J.4. Dianlscements in terms of strsases in the . ~ ~- -~~~

membem.-5.6. J)iaylarr!mentsaf beam by strain energy methods.-4.6. Calculation of reartions ia eontinnroua beams and gd<,m.--5.7. Oalmlation of the angle of rotation.-6.8. \\'illioIt-Mohr dirrplmment diagrams . . . . . . . . 66

CHAPTER 6

STRESS ANALYSIS OF REDUNDANT FRAMES

6.1. Introduotion.4.2. Streas analysis by direot mmpariaon of displace- menb.4,3. Stresees in framea with one redundsncy.-4.4; Sirein energy analysis for framea with more than one redundant element.4.5. Stresses due to changes in temperature.--6.6. Diatrihution method. of streas analyeis applied to pin-jointed framas.4.7. Southwell's re- laxation method.--8.8. Choice of method of stress sndyaia.4.9. Design of redundant framea.4.10. E 5 c t of curved ham in a frame- work.4.11. Principle of supelmition applied to redundant frameworks 85

CHAPTER 7

STRUTS AND LATERALLY LOADED COLUMNS AND TIES

7.1. The behaviour of struts under loed.-7.2. The critical load for slender struts.-7.3. EocentricaUy loaded strut.-7.4. Stocky atrub.-7.5 General atrut formulae.-7.6. Mdilied-Smith formula for pin-jointed struti-7.7. To construct s o w e representing Smith's mcdified, formula.-7.8. Defleotion of B strut.-7.9. Perry atrut formula.-7.10. Members with combined losde.-7.11. The 'pn.jointed strut with s uniform Intern1 load.-7.12. Pin-jointed 8 t ~ t with a concentrated lateral load-7.13. Strut with end couplea.-7.14. Pin-jointed strut with two lateral losda.-7.15. Enoeatd strut with a uniform bteral load.-7.16. Encestd strut with a central lateral load.-7.17. Perry's appruximntion for a pin-jointed strut with uniform lateral load.-7.18. Approximatd fonnulea for laterally loaded ~truts.-?.19. Members with combined bending and end tensions.-7.m. Initially curved strut with end am lea. 7.21. Polar diagrams for beams with end thm&s.-7.22. Deri- 124 vat% n of - ~ t r ~ t t o r m ~ fmm po~m diagmms .

CHAPTER 8

CONTINUOUS BEAMS AND C O L W S

8.1. The general problem of the continuous beam.4.2. Wihn 's method. 4 : 3 . The theorem of three moments.-8.4. Moment distribution method.-8.6. The generalised theorem of three moments.--8.6. The continuous colump . . . . I68

CHAPTER 9

FRAMES WITH STIFF JOINTS . 9.1. Stiff j0inta.-9.2. Strain merw nnalyaia of &S-jointed frames.-9.3.

Slope deflection analysis of rigidly jointed frames.-9.4. Slope deflec- tion analysis of frama with aeini-rigid joints.-4.5.' Moment distribution method . . . . . . . 190

CONTENTS vii

CHAPTER 10

SECONDARY WRE&SES IN FRAMED STRUCTURES l PAGE

l 10.1. Secondary etresaes. Slope deflection method of analysis.-10.2. Moment dmtribubon methodof analysia . . . . . 233

I CHAPTER 11

1 THE BEHAVIOUR OF COMVECTIONS IN STEEL FRAMES i 11.1. General description of the behaviour of connections.-11.2. Effect of I the behaviour of connections on the design of a frame . . . 242

CHAPTER 12

1 ELASTIC ARCHES AND RINGS I

12.1. Action of the arch.-12.2. General t-.-12.3. The three-pinned arch.-12.4. Bending moments in a t b - p i n n e d arch.-12.5. The two.pinned arch.-12.8. Two-pinned segmental an?h rib : strain energy anslysis.-12.7, Two-pinned prsbotic eroh.-12.8. Two-pimed arch;

1 p p h i c s l solntion of equations.-12.0. Analysis pf two.pinned arch ? from strain equations.-12.10. Resultant &ions in two-pinned arch.-

12.11. Arohed rib with tired ends.-12.12. S p m e t r i d y baded amh rib 6xed a t ends.-12.13. Applioation of principle of superposition fo 6x4 amhen.-12.14. The h r d arch.-12.16. Temperature stmmea in . an arch.-12.18. The ciroular rinp.-12.17. Stresses in a brsoed ring. 263

CHAPTER 13

THEORY OF COMPOSITE STRUCTURES AND REINRORCED CONcRrnE

13.1. Simple composite members.-13.2. General principles of reinforced wncmte.-13.3. The raota.n& rainford concrete beam with tension reinforcement.-13.4. The reinforced conoreta T-beam with temion reinfwcement.-13.5. Rectangular besm with campreasion reinforce- ment.-13.8. Adheaion end bond.-13.7. Distribution of ahem at- in a reinforced concrete beam.-13.8. Shear reinfwment in besms.7 13.9. Elexural stilheea of reinforce3 ooncrete membem.-13.10. The asidly loaded reinforced concrete column.-13.11. Reinford concrete members subjected to mmbioed bending snd axial load.-13.12. Strength of materisle and rdlowahle stmmea . . . . 287

CHAPTER 14

INPZUENCE LINES FOR STATICALLY DETERWXATE STRUCTURES

14.1. Delbition.-14.2. Influence linen for a simply supported beam.- 14.3. Smgle rolling load on a simply supported beam.-14.4. Dis- tributed mlling load on simply supportad beam.-14.8. Two con- centrated loadn on simply supported beam.-14.6. Any number of beds an a hmm.-14.7- In0uwea lioee for framed atrndlvfg.-14.8. -~~~~~ ~~-

Influeno. li-~for three.pinned &2h.-14.~~Convent ioad~d sg.tema. -14.10. Dynsrnicd loads on bridgee.-14.11. Colcubtion af impwt abwance on rdway W . - 1 4 . 1 2 . InBuence linen of delleation 316

viii CONTENTS

CHAPTER 16 INFLUENCE LINES FOR STATICALLY INDETERMINATE

STRUCTURES PAUQ

16.1. Use of influence lines.-15.2. Miiller-Bm1avU8 thmmm.-16.3. In. fluence lines of reaction for continuoua girders.-15.4. Influence line of shearing force for a continuoua girder.-16.6. Wuence line of hen* moment for a continuous girder.-16.6. Influence lines of resations for a continuous truss.-16.7. Influence line of foroe in a continuous truas. -16.8. Foma in redundant bars by influence &W-.-16.9. In- fluence line of thruat for two-pinned arch.-15.10. Influence line of bendingmoment for a two-pinned arch.-16.11. Influenceliaesfor a W arch.-15.12. Choice of redundant elements to simplify calculations 357

CHAPTER 16

THE SUSPENSION BRIDGE

16.1. The hanging cable.-16.2. Stiffened suspension bridges.--l6:3. Sus- pension bridge with three.pinned stiffening girder.-16.4. Influenoe lines for bridge with threapinned sti5ening @er.-16.6. E h t of uniform load on thres-pinned stitlening girders.-16.6. SUB@D~ bridge with two-pinned stiffening girder.-16.7. Influence line of bending moment for two-pinned girder.-16.8. Influence line of sheating force for two-pinned girder.-16.9. Length of s suspension

r cable.-16.10. Deflection t h m v of suspension bridges.-16.11; Streeeea in an extensible sus@on cable . . . . , 381

CHAPTER 17

THE BEAM CURVED IN PLAN

17.1. The curved oanti1ever.-17.2. The circular am bow girder.-17.3. Circulsr arc bow girder with s distributed load.-17.4. The bow @er of any a h a p with a concentrated load-17.6. Bow girder of anrahepe with distributed 1d.-17.6. Deflection of a bow girder.-17.7. Bow girders having symmetry about an axis.-17.8. Bow @er with inter msdi~te 8npports . . . . . 411

CHAPTER 18

NOTES ON FLAT SLABS AND PLATES

18.1. Qenera1.-18.2. The circulas plate.-18.3. The motangular slab 429

CHAPTER 19 THE DESIGN OF STEEL FRAMED BUILDINGS .

19.1. Intmduction.-19.2. W t i n g deaign methods.-19.3. Prsliminsry in- vestigation. by the S h l Stmctnres Betesesrch Committee.-19.4. Review of teats on bui1dinga.-lB.6. The problem of design.-19.6. Evolution of a mathod of dasign. . . . . . . . 436

INDEX NOTE.-Refereacea are to p g e numbers.

, Adhesion in reinforcedconcrete, 297 Aeronautical Research Committee, 155 Airship fin rib, a l y s i n of, 97

transverse frame, 284 Analysis of voussair arch, 694 Angular'rotation of beam, calculation by

strain energy, 77 Arch action, 263 Arch, *slyme of two-pinned from strain

equations, 266 braced, 277 ., encastd, influence lines, 375 -, symmetrically loaded, 272 graphical solution of two-pinned, 263 iniluence lines for three-pinned, 336 linear, 268 pambolic twa-pinned, 262 piinciple of auperpoaition applied to,

273 resultant action. in two-pinned, 267 rib, 254 -, encmtd, 268 temperature stresses, 279

: tbree-pinned, 255 two:pinned, 258 -, influence line of moment, 374 -, influence thrust line, 371 typcs, 264

Arching of granular material, 516 Atcberley, L. W., 489,605,608 Atkinaon. 403 Atwood, 570 Austrian Society of Engineers, arch

experiments, 574 Axial force, modified by end moments,

237 Axial thrust in loaded beam connected

to stanohione, 450 ~Ayrton and Perry, eooentric load on

struts, 135

Baker, Sir Benjamin, 536 Barlow, 571 Barrel of arch, 669 Batho. C.. 251.459

Ream, continuous. reactions by atrain ene'gy, 76

deflection of, 28 deflection under comentmted load, 30 - under couple, 34 -under dietributed load, 32 design method, 469 deaign; propoaais of Steel Stmctures

Raaeamh Committee, 460 displacements by strain energy

methods. 12 enceatr6. 36 Aitched, 288 king-pasted, 95 of varying section, 38 slopes calculated by strain energy, 77 slopes under load end end couples, 35 twiat under unsymmetrioel Wing, 26 with flexible connectione, stresses in,

251 Besms, plaatic behaviour of propped, 603 Beggs, Q. E., 654 Beggs' deformeter, 556 Bending moment, 21

-, hogging, 30 * - in tbree-pinned arch, 257 of curved beam, 40 strain energy, 64 theov of, 22 under oblique loads, 24 .msymmetricel, 26

Beny. Arthur, 184 Beny functions, B16 Block displeoements. 110 Boistaml. 670 Boles, H., 184 Bolted connections, 248 Bond in reinforced concrete, 297 Booth, H., 184 Bow girder, ansllysin by atrsin energy

methods. 413 any shape with ooncentrsted load, 417 any shape with dietributed load, 423 I o*lar-av, 412 cmular. with distributed load, 416

Beam, bending of o w e d , 40 deflection of, 424 continuous, 168 symmetrical, 426 -, moment distribution method, 176 with intermediate supports. 427

621

Clothing of steel framed buildinga, effect

622 INDEX

of, 462 Code of Practice for reinforced conemte,

293,302,307,308 for steel buildings, 435

Column analogy, 40 Column, continuous, 188

in reinforced concrete, axinlly loaded, 306

Compatibility of strains, 85 of stresses, 85

Composite members, 287 Comprwion reinforcement in concrete

Braced areh, 277 Y ' Y ~ O ~ S 284 m, rtnrrsea in, 284

Bridge classitioation, 346 dynamical loads on, 344 impaot hotor, 344 railway, impact allowance, 346 -, long span, 346, 348 -, medium span, 380 -, short pan, 361

Bridge Strees Comrnittee,'344 Building frame, experimental, 441

steal, 435 Building Reseercb Station, experiments

on vouasoir mhes, 676 Butler. E. W., 457

Cable, hsnging, 381 Cantilever, c m e d in plan, 411

deflection under uniform load, 29 arry-over factor, 212, 223

moments, 179 Case, John. 430 Casing of stanchions, effect on stream,

462 Castigliano, h t theorem, 69

w n d theorem, 60 theorems applied to moments, 62 treatment of vouasoir m h , 572 use of first theorem to ealculrrte dis-

placementa, 68 Choice of analytic method, 110

of redundenoiea in analyeia, 376 Circular arc bow girder, 412

plate, stresses in, 430 ring, 280

Clapeyron, theorem of three momonta, 170

Cl~iIication of structures, 1 Cleated conneotion, 246 Clerk hxwell , reciprocal theorem, 67 -, uae of in experimental analysis,

664

beams, 296 Concrete, reinforced, prinoiples of, 288

Connections, behaviour of. 242 bolted, 248 charaek~iatic curve replaoed bg

chords, 248 effect of flexibility on beama, 261 effect of on frame deaige, 248 encased in conorete, 247 hnge-cleat, 246 riveted, 248 slip, 246 split I, 247 testa of in actual buildings, 447 web-aleat, 246 welded, 248

Continuous beam and girder, m~otiana by strain energy, 75

-general problem, 158 - moment dintrihution method, 176 - Wilaon's method, 169 column, 188 girder, influence line of bending

moment, 365 -, inffuence line of shear, 364 -, influence lines of reactions, 359 stanohion, plastic behaviour, 605 truss, influence lines of force, 367 -, inlluenoe line8 of reactions, 366

Cwk, G., 596 Cooper conventional load system, 340 Couplet, 570 Critical load for strut, 126 Croes, Hardy, 40, 101, 211 Crosthwaite, P. M,, 516 Crown of arch, 569 Curvature formula for strut, 132 Curved bar, equivalent modulus, 116

bars in frame, 114 beam, bending of, 40 -, modified area of oross section, 42 -, strsin energy of, 66 cantilever. 411

Cutler, see Thompsan and Cutler, 236

Conjugate pressures, 572 at-S. 621

Dam, function of, 488 pmfle, analysis of, 493 -, Rankine, 496 -, Wegmann, 497 Rankine's oonditions, 489 Saeilly's rules, 489 shearing dintribution, 505 d e s on vertical sections, 508 types of, 488 - hilure, 488

Defleotion, iduence lines, 351 of beams, 28 of strut, 131

Deformeter, Beggs', 656 Dasign of redu. Lent framea, 110

of steel building *amen, 438

Muenoe lmea for t h . p i n n e d stiffening girder in suspension bridge, 389

-, mechnnioal plotting, 654 - of bending moment for continuaus girder, 386 - of deflection, 361

-of fome in continuous truas, 367 - of moment for two-pinned m h , 374 - of moment for two~pinned stiffen-

ing girder, 399 - of reaetion for continuous girdem, 369 - of reactions for continuous trusa, 366

-of &ear for contimuous girder, 364 - of shear for tm.hqed stiffening

girder, 401 - of thrust for two-pinned m h , 371 -L of t h t for two-pinned pambolio

m h , 372 -, simple mwha.nica1 determination.

640 - W, C. E., 345,346,432, 610 Institute of Welding, 600,608 Intradw of arch, 569 '

Jenkin, C. F., 616 theory of earth p m u r e , 530

Joints, stiff, 100 Just-atiff fmme, 3

Keptone, 588 King-posted beam, analysis of, 96

L a t e d y ldaded etrut, 131 -, approximate formulas, 141

Laterally l d e d tie, 147 Lea, F. C., 369,367 Leaat work, principle of, 82 Linear m h , 288

--, o o m t one for vouesoir arch, 673 Load hctor, 2,136 - applicable to s k l framed building,

467 ayatam, eonv~ntio~ul , 339

Long spsn bndge, 346, 348 Love. A. E. H., 432

Mucaulay, W. H., 32 Mnnderla, treatment of saeondary

strews, 240 Maney, G. A., 6.51 Masomy m b , behaviour. 682

-S doe under Vouesoir m h . Mwonq dam, at- diatribntion in,

481

EX M m structures, dehition, 2 &terials for reinforced concrete, Maximum bending moment under

loads, 326 Meohanical analysis of at& in pi

frames, 648 determination of inhence lines, dope defleutiou analysis, 651

Medium span bridge, 346.360 Meem, C. J., 516 M e h , J., 403 Mery, 670 Method of resolution, 12

of saetions, 10 of tension ooefficienta, 13

Ministry of Transport mdiioation Pencoyd formula, 344

requirements for highway Modified area of curved bea

construction, 44 of motion for initidly ourved k m ,

Modular ratio, 289 Mohr diaplaoement diagram, 80 Moment area method, 39 Moment, bendurg, 21

distribution analysis of .sec0 a t m w a , 235 - factora in members with semi- joints, 223 - methcd spplied to contim

bcam, 176 - method applied to frame, 211 - method for frame with se

jointa, p1 effect of end on axial fo-, 237 of resistance, 23 of resistance of reinforced oo

beam, 291 restraiuii in encnstr4 beam, 36

Moselsy, 571 Miiller.Brealnu, I3

theorem, 361

Navier, 670 --, formula for amh, 671

Oblique loada on beam, 24

Parabolic m h , two-pinned, 262 two-pinned am& Suenoe line

thrust, 372 Penooyd impact formula, 344 Penraon, Knrl, 488,492,505,508 Perrouet. 670 P e w and Ayrton, eccentric 1

a+t, 136 Perry, approximate formula for la

lmded strut, 146 Pew, J. , strut formule, 132

/ Pigmud, M,, 433 i Pleatic behaviour of oontinuou~ : stanchion, 605 ' - portal fmme, 600 ,

- propped beams, 803 - reinforced concrete structure, 611 - simply supportedbeam, 596

Plastic rmga in structum, 596 Plate, cironlar, atwses in, 430 Polar diagrsrn for laterally loaded swta,

166 Polar diagrams used to derive strut

formuh, 161 Portal frame, Institute of Welding testa,

600 -, plsstio behaviour, 600

k o t t , J.; 431 Pressure triangle, 528 Rimmy stresses, 6 Principal axes of inertia, 25 Principle of bast work, 62

of Saint Vensnt, 63 of superposition, 48 - applied to arches, 273 -applied to redundant frn~me8, 117

Profile for retaining wn11, determination of, 638

Propped beams, plastic behaviour, 603

Rankine, arch theory, 571 Rsnkine dam profile, 496

on design of dams, 489 strut formuls, 128 theory of earth pressure; 517 -of foundation depth, 518 - of retaining walls, 620 -of surcharged retaining walls, 622

Ratio, modular, 289 Ratzedorfer, J., 156 Reactions in continuous beenla and

girders by strain energy, 75 Reactive forcea, 4 Reciprocal theorem of Clerk Mnxwell, 67 Rectangular slab, stresses in, 431 %dundant forcea determined by in-

fluence diagrams, 369 frame, 3 -, design of, 110 frames, application of principle of

suprpositian. 117 Reinfomad cancrete;adhesion and bond,

297 h m , doubly reinforced, 295 -, moment of resistance, 291 -, tension reinforced,M Code of Practice, 293, 302, 307, 308 oolumn, axially losded, 306 flexural stiffness, 305 member, combined bending and axhl

load. 308

INDEX 625

Reinforced concrete, plastic behaviour. 611

principles of, 288 shear dietribution in beam, 299 shear minfomement, 301 strength of materials, 309 T-beam, 293 -, approximete treatment, 294

Reinforcement,, eoonomic percentage, 291

Kelation between laadiug, bending moment and shear, 21

Relaxation method of streae analysis, 106 Rennie, 670 Repeated loading of voussoir arch, 588 Reaistanc.e, moment of, 23 Resolution, method of, 12 Restraining moments in encastd beam,

36 Retaining well, application of Ranhe 's

theory, 520 determination of profile, 536 surcharged, Rt~nkine's theory, 522

Reynolds, Osborne, 615 Rib, arch, 254

sncaatd arch, 268 Rieckhof, C., 654 Rigidly jointed frame, slope deflection

analysis, 199 Ring, b r d , strews in, 28$

cirrular, 280 Rings, experimental analysis, 562 Ritehie, E. G., 412 Ritter, method of aeotions, 10 Riveted oonnections, 248 Robortson, A., 134, 596 Robison, 670 Rolling load, distributed on simply .up-

ported beam, 318 single on simply supported ~ L I I I I , 317

Rolling loads, critrrion for load lmitian for maximum shear, 327

maximum bending moments due to, 326

maximum farces in franlea due to, 335 on beam, geneml case, 325 two on simply supported beam, 322

Rondelet, 670

Safety, factor of, 2 Saint Venant, principle of, 63 , Sazilly, design of dam, 489 Soott, W. L., 433 Secondary stress analysis by moment

distribution method, 235 - by slope defleotion method, 223 eccentric joints, 230 effect of weight on menlbera, 239

Secondary strews, 5

636 Second theorem of hatigliano, 60 Sections, method of, 10 Segmental -h, two-pinned, 268 Self-&mining, 5

stresses, calculation of, BO Semi-rigid joint, 208

moment aistrihution applied to fra~nes with, 221

Shear area method, 39 Shearing fom, 21

strain energy, 55 Shear reinforcement in reinforced cot,-

crete beams, 301 stress, distribution in buam, 26 -, distribution in reinforced concrete

beam, 298 Short span bridge, 346, 361 Simply supported beam, plastic be-

liaviour, 596 S i l e curvature bending of struts, 446 Single rnlling load on simply supported

beam, 317 Skeleton frame, 2 Skew arch, 969 Skcwhok, 569 Slab, &t, 429

rectangular, streaeea in, 451 Slater, W. A., 433 Slendemese ratio of strut, 124 Slender strut, 124

critioal load, 125 Slip in structural connections, 245 Slope deflection analysis of frame with

semi-rigid joints, 208 -of secondary stresses, 233 n~eohnnioal analysis, 561 method for stiff-jointed frame, 199

Slope of beam by stmin energy method, 77

under loaas and end couples, 34 Smith, It. H., strut forinula, I29 Snell, 571 Soffit of areh, 569 Southwell, R. V., 13, 63, 105, 129, 131,

233,403 Spandrel of arch, 569 Split I connection, 247 Springing of sroh, 569 , Stability of voussoir arch, 5BO Stanchion, design of internal, 469

Steel Structures Research Committee's rules for design, 480

width, effeot of on strese analgais, 228

worst load conditions, 455 Stanohions, Institute of Welding testa,

BOB Steel buildins fi.amu, design mothods in

use, 436 tests on. 446

INDEX ? Steel framed building, design problem,

453 ' d e o t of clothing, 462 effect of flmra, 461 effeot of stanchion casing, 452 evolution of design method, 457 use of load factor, 457 wind loade, 483

Steel Structures Research Committee, 1

135,1SS,435,441,460,480 Steinm~nn~ D. B., 403 Stiffenera, web, 246 Stiff joint, 190 Stiff-jointed frame, plastic behnviou~,

610 1 -, strain energy anelysie, 192

Stiffnese of a member, definition, 177 'Stocky strut, 124, 127 Strain compatibility, 85 l

energy as function of external loads, 53 -, definition, 51 i -due to shear. 55 - in terms of tension coefficients, 64 - of bending, W -of curved beam, 56 -of torsion, 55

Stress anslysie by conlpariaon of din. placements, 86

-by relaxation method, 105

1 -, choioe of method, 110 , -, distribution methods, 101 -, meohanical. for pinned frames, 648 . compatibi!ity, 85 diagram, 7

Strasses, conjugate, 621 due to temperature, 99 in fiamea with one redundancy, 87 in masonry dam, 491 primary, 5 accondary, 5

Stmyer, R. N., 5Ui Structure, behavhr in plsatic rahge, 506 Strut, behaviour Gf, 124

oriticel load, 1% curve for Smith's form&, 130 deflection of, 131 double cwature bending, 444 effective length allowed in steel build.

ing frames, 439 effective length in rigid-jointed frame,

439 unoastd with central load, 145 -with uniform lateral load, 144 . formulas derived from polar dia.

grams, 161 general formulas, 128 initially curved with end couples, 148 Perry formula, 132 polar diapme, 155 Rmkine formula for, 128

&rut, Robertaon's tests on, 134 single ourvature bending, 446 dender. 124 slendern8am ratio, 124 Smith's formula, 129 m k y , 124, 127 with eccentric load, l26 with end oouplea, 142 with lstaral loads, 137 - approximate formulas, 147 -, Peny appmximation, 146 with two lateral loads. 142 ~- ~

Superposition, principle 'of, 48 -; *pplied to arches, 27a , applied to encsetd h&, G0 -, applied to redundant frames, 117

Snapension bride, deflection theory, 403 elastic theory of, 386 intluence linen for three-pinned girder,

388 stiffened, 383 b . ~ i n n e d girder, 384 unstiffensd, 381 with three-med girder under y i -

form W, 302 with twspinned girder, influence

line of bending moments, 399 with two-hinged stiening girder,

Muenoe line of shear, P01 Snapemion cable, extensible, 405

l& of, 402 Swty in iname, 202.219

Twisting of beam under unapmetrioal bending, 26

Two-pinned arch, 268 - analysis from strain equations, 266 -, gmphicsl solution, 263 -, resultant actions. $87 parabolic arob. 262 segmental arch, analysis by strain

e r y y methods, 258 Two rollmg loads on simply supported

beam, 322

Umymmetrical bending, 26 Unwin, W. C., 492, €85 Uplift pressure on damn, 489

Vauasoir, 568 Vousaoir arch, 568 -, sooepted basis of design, 573 -, analysis and design, 594 -, as elaatio structure, 574 -, correct liqear smh, 673 -, experiments by Austrian Saoiety

of Engineers, 674 -, experiments by Building &search

Station, 576 -, experimental m a r o h , 575 -, meohanics of, 577 -, middle-third rule, 687 -, repeated load teats, 688 -, stability, 680

T-beam in reinforced concrete, 283 Web-olat tonneetion, 216 - approximate treatment, 294 Web stiffener, 245

Temperaturn uhesaeB, 99 Wedge thenry of earth pressure, 520 in arch, 279 Jenkin'a revision, 530

Tension ?ae5oienns, method of, 13 Wegmann, E., 497 atrain energy ia terms of. 64 Weight of members in ssoondary stress

Tests on steel building frames. 446 analysis, 239 Theorem of three momenta. 170 Welded connection, a48

in generalised form. 184 Weeamnn, H. E., 211 Theory of bending. 22 Weatergad, H. M., 433 Thompeon and Cutler, 236 Width of stanchion, effect of in atresa Three moments theorem, 170 ana?ysis, 228 Three-pinned m h , 285 Williot displaoement diagram, 78

bending mbments, 257 Wilaon, G., 169 Thrust in beams in ateel h m e d build- Wilson, W. M,, 651

in@, 450 Wind load on steel building frames, 483 Tie with Isteral l d , 147 Wind p m u r e on steel building frames, Timmhenko, S., 403,404 438 Torsional atrain energy, 65 Winkler, 41, 572